The A10 [Datsun 1000] flywheel starts out as quite noticeably the lightest of all the A series flywheels, but it came with a smaller clutch & it had a groove machined into the face just outside the clutch disc.

With mine, we removed the dowels, then machined the whole face down to the bottom of this groove to leave a single flat face. We then drilled & threaded the flywheel for the larger A series clutch. [1200 & onwards] Next we took some material from the back to make it a bit tidier, & even lighter.

End result? A surprisingly light flywheel for a relatively small amount of work & money.
Now, 25 years later, it it intended that it will go onto my A13 engine with yet another new Sunny Wagon clutch, for my coupe. Waste not, want not. At least, that's the plan.

Mildman.
I'm sure that you must have weighed two A12 flywheels as I have compared an A14 & A12 flywheel before. Just picking one of each up in each hand immediately told me that there was a very noticeable difference.
Even the heaviest of the A series flywheels can be lightened down to the same weight as a lightened A12 one, it just takes a bit more work to remove the extra material, & if you are paying for it by the hour, then it will obviously cost a little more.